Puzzling Prattle (by Sam Loyd)

Two children, who were all tangled up in their reckoning of the days of the week, paused on their way to school to straighten matters out. “When the day after tomorrow is yesterday,” said Priscilla, “then ‘today’ will be as far from Sunday as that day was which was ‘today’ when the day before yesterday was tomorrow!”
On which day of the week did this puzzling prattle occur?